Natural Selection. DNA encodes information that interacts with the environment to influence phenotype

Transcription

1 Natural Selection DN encodes information that interacts with the environment to influence phenotype mong The Traits That Can Be Influenced By Genetically Determined Responses to the Environment re: 1. The Viability in the Environment 2. Given live, the Mating Success in the Environment 3. Given live and Mated, Fertility or Fecundity in the Environment. 1

2 10/16/12 Viability Hb-β Locus In frica: Non-Malarial rea / No nemia /S S/S No nemia nemia Viability: High High Low Malarial rea Not Resistant to Malaria Resistant nemia Viability: Low High Low Mating Success Normal Diet Mentally Retarded Institutionalized Low Chance of Mating Low Phenylalanine Normal Intelligence Diet High Chance of Mating p/p fetus develops in Low Phenylalanine in utereo Environment p/p Baby Born With Normal Brain 2

3 Fecundity/Fertility H/+ In Society With No Birth Control, No Genetic Literacy, and Low Expected Lifespan: Normal Fecundity H/+ In Society With Birth Control, Genetic Literacy, and High Expected Lifespan: Low Fecundity Why re Viability, Mating Success, and Fecundity/Fertility Important Phenotypes in Evolution? Because ll Of These Phenotypes Influence The Chances For Successful DN Replication 3

4 Physical Basis of Evolution DN can replicate DN can mutate and recombine DN encodes information that interacts with the environment to influence phenotype Physical Basis of Evolution Viability Mating Success Fecundity/Fertility DN can replicate DN can mutate and recombine DN encodes information that interacts with the environment to influence phenotype 4

5 Physical Basis of Evolution DN can replicate DN can mutate and recombine DN encodes information that interacts with the environment to influence phenotype Viability Mating Success Fecundity/Fertility These re Combined Into Single Phenotype of Reproductive Success Or FITNESS DN can replicate DN can mutate and recombine Genotypic Variation In Demes and Species Heritable Variation In Fitness Phenotypic Variation In Fitness Environment 5

6 Natural Selection Is Heritable Variation In Fitness That Is, The Genes Borne By Gamete Influence The Probability of That Gamete Being Passed On To The Next Generation. THINK LIKE GMETE! NTURL SELECTION IS NOT CIRCULR DN can replicate DN can mutate and recombine Genotypic Variation In Demes and Species Heritable Variation In Fitness Phenotypic Variation In Fitness Environment 6

7 Natural Selection t Single Locus in Randomly Mating Deme Zygotic Frequencies Environment Viabilities dult Frequencies Environment Mating Prob. Mated dult Frequencies Environment ve. No. Offspring Mated dult Frequencies Weighted By No. of Off. p 2 a 2pq aa q 2 V V a V aa p 2 V a 2pqV a aa q 2 V aa C C a C aa p 2 V C a 2pqV a C a aa q 2 V aa C aa b b a b aa p 2 V C b a 2pqV a C a b a aa q 2 V aa C aa b aa Let W = V C b ; W a = V a C a b a ; W aa = V aa C aa b aa Zygotic Frequencies Environment Fitness p 2 W a 2pq W a aa q 2 W aa Mated dult Frequencies Weighted By No. of Off. p 2 W a 2pqW a aa q 2 W aa Convert to Freq. By Dividing by μ=w = p 2 W +2pqW a +q 2 W aa Mated dult Frequencies p 2 W /W a 2pqW a /W aa q 2 W aa /W Meiosis 1 1 / 2 1 / 2 1 Gene Pool p = p 2 W /W + pqw a /W a q = q 2 W aa /W + pqw a /W 7

8 Gene Pool p = p 2 W /W + pqw a /W a q = q 2 W aa /W + pqw a /W p = p 2 W /W + pqw a /W =( p 2 W + pqw a )/W p = p(pw + qw a )/W Does Evolution Occur? Δp = p - p = p(pw + qw a )/W - p = p[pw + qw a )/W - 1] Δp = p[pw + qw a -W]/W 8

9 Does Evolution Occur? Note, W = W(p+q)=pW+qW Δp = p[pw + qw a -W]/W =p[p(w -W)+ q(w a -W)]/W Since p and W are always > 0, This is the only part of the equation That Can Change Sign and Hence Determine the Direction of Evolution Under Natural Selection. Does Evolution Occur? What is: p(w -W)+ q(w a -W)? Mean Phenotype of Fitness 9

10 Does Evolution Occur? What is: p(w -W)+ q(w a -W)? Genotypic Deviations for the Phenotype of Fitness Does Evolution Occur? What is: p(w -W)+ q(w a -W)? This is the verage Excess of the llele for the Phenotype of Fitness 10

11 Does Evolution Occur? Δp = pa /W Natural Selection is n Evolutionary Force Whenever p 0 or p 1 (that is, there is Genetic variation) and when a 0 (that is, When there is heritable variation in the Phenotype of fitness). To Understand Natural Selection THINK LIKE GMETE! 11

12 Sickle Cell nemia In frica n Example of Natural Selection The Sickle Cell Mutation 12

13 Infection of a Red Blood Cell By a Malarial Parasite Sickle-Cells re Filtered Out Preferentially by the Spleen Malaria Infected Cells re Often Filtered Out Because of Sickling Before the Parasite Can Complete Its Life Cycle The Sickle Cell llele is Therefore an utosomal, Dominant llele for Malarial Resistance. The Sickle Cell nemia Phenotype 13

14 Most Deaths Due to Sickle Cell nemia and Due to Malaria Occur Before dulthood. Viability Is The Phenotype of Living To dulthood In a non-malarial Environment, The S llele is a Recessive llele For Viability Because Only the Homozygotes Get Sickle Cell nemia. In a Malarial Environment, The S llele is an Overdominant llele For Viability Because Only the Heterozygotes re Resistant to Malaria nd Do Not Get Sickle Cell nemia. 14

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16 ICELND MDGSCR 10/16/12 Two Complications to This Simple Story in frica: 1. Epidemic Malaria is Recent to Most of Wet, Tropical frica and the Process of daptation to Malaria in frica Is Still Not in Equilibrium. 2. There is a Third llele, Hemoglobin C, Involved in the daptation to Malaria in frica. Epidemic Malaria in frica bout 2000 years ago, Malayo-Indonesian Colony Was Established on Madagasgar 16

17 Epidemic Malaria in frica This Colony Introduced The Malaysian gricultural Complex into This Region Epidemic Malaria in frica This gricultural Complex Was Taken Up By Bantu- Speaking Peoples, Followed by Large Expansion of the Bantu In frica bout 1500 years go. 17

18 The Malaysian gricultural Complex In frica Is associated with slash-and-burn agriculture: Provides habitat and breeding sites for nopheles gambiae, the primary mosquito vector for falciparum malaria. Results in the high local densities of human populations that are necessary to establish and maintain malaria as a common disease. Epidemic Malaria in frica 18

19 The Hemoglobin C Mutation Hb- GG Glutamic cid 6 th Codon Hb-S GTG Valine Hb-C G Lysine The Hemoglobin C Mutation Hb-C Is Recessive llele for Malarial Resistance 19

20 Hb-, S and C Genotypes S SS C CS CC nemia Malarial Resistance Viability No Malaria No No Yes (Severe) No Yes (Mild) NO No Yes Yes No Yes Yes Hb-, S and C Genotypes S SS C CS CC nemia Malarial Resistance Viability No Malaria No No Yes (Severe) No Yes (Mild) NO No Yes Yes No Yes Yes The and S lleles Define n utosomal Recessive Genetic Disease: Selection Will Insure it is Rare But Difficult to Eliminate in a Random Mating Population. 20

21 Hb-, S and C Genotypes S SS C CS CC nemia Malarial Resistance Viability No Malaria No No Yes (Severe) No Yes (Mild) NO No Yes Yes No Yes Yes The and C lleles Define Set of Neutral lleles in a Non-malarial Environment: Their Frequencies re Determined by Genetic Drift and Mutation. Hb-, S and C Genotypes S SS C CS CC nemia Malarial Resistance Viability No Malaria Viability Malaria No No Yes (Severe) No Yes (Mild) NO No Yes Yes No Yes Yes Observed Relative Viabilities In Western Tropical frica 21

22 Hb-, S and C CC is the Fittest Genotype By Far If Natural Selection is Survival of the Fittest, Then Natural Selection Should Increase the Frequency of the C allele and the CC Genotype. Contrary to Rumor, Natural Selection is Not Survival of the Fittest. Natural Selection Is Heritable Variation in Fitness, so Think Like Gamete: Which Gamete Has the Highest verage Excess of Fitness? Initial Gene Pool Before Malaria p = 0.99 p S =.005 p C =

23 Initial ve. Fitness fter Transition to Malaysian gricultural Complex p = 0.99 Under Random Mating, the Mean Phenotype = W = p S =.005 p C =.005 Initial Phenotypes fter Transition to Malaysian gricultural Complex p = 0.99 p S =.005 p C =.005 Genotypes S SS C CS CC Viability Malaria Genotypic Deviation (W = 0.901)

24 Initial Phenotypes fter Transition to Malaysian gricultural Complex Genotypes S SS C CS CC Viability Malaria Genotypic Deviation (W = 0.901) a = a S = a C = Initial Phenotypes fter Transition to Malaysian gricultural Complex a = a S = a C = The Initial daptive Response To Malarial Environment Mediated By Natural Selection Is To Decrease, Increase S, and Leave C The Same (Δp x = p x (a x )/W) 24

25 Gene Pool fter Several Generations of Selection Under Malarial Environment p = 0.95 S W = p S = p C = Gene Pool fter Several Generations of Selection Under Malarial Environment p C =.005 p = 0.95 S.045 Genotypes S SS C CS CC Viability Malaria Genotypic Deviation (W = 0.907)

26 Gene Pool fter Several Generations of Selection Under Malarial Environment a = a S = a C = fter the Initial daptive Response To Malarial Environment, Natural Selection Continues to Decrease, Increase S, but Now It lso Decreases C Because a C = Gene Pool fter Several Generations of Selection Under Malarial Environment p C 0 p 1-p S S p S Genotypes S SS C CS CC Viability Malaria s p S increases in frequency, W increases and these Genotypic Deviations Become Increasingly Negative. Therefore, Natural Selection Eliminates the C llele. 26

27 Selective Equilibrium Will Only Occur When Δp = 0 Under Natural Selection For ll lleles. p = 1-p S S p S Genotypes S SS Viability Malaria a = (1-p S )(0.9-W)+p S (1-W) = 0 = a S = (1-p S )(1-W)+p S (0.2-W) Selective Equilibrium Will Only Occur When Δp = 0 Under Natural Selection For ll lleles. p = 1-p S S p S a = (1-p S )(0.9-W)+p S (1-W) = a S = (1-p S )(1-W)+p S (0.2-W) (1-p S )(0.9)+p S (1) = (1-p S )(1)+p S (0.2) p S = 1-0.8p S 0.9p S = 0.1 p S = 0.1/0.9 = 0.11 So t Equilibrium, p S = 0.11 and p =

28 The Equilibrium llele Frequencies re Maintained By Natural Selection, Resulting in a Balanced Polymorphism p = 0.89 S p S =0.11 The Balance Occurs Because When p S < 0.11, a S > 0 (malarial resistance dominates the average excess) nd When p S > 0.11, a S < 0 (anemia dominates the average excess) The Equilibrium p = 0.89 S p S = S 0.20 SS 0.01 W = 0.9 W S = 1 W SS =0.2 t Equilibrium, There is Genotypic Variation in Fitness (Broad-Sense Heritability), but No Heritability (verage Excesses = 0). 28

29 daptation By Natural Selection Depends Upon History: Which Mutations re Present and Their Frequencies. The course of adaptation is always constrained by the available genetic variation and proceeds until there is no heritability of fitness. Two Possible Responses to Malaria p 1 p S 0 p C 0 p = 0.89 S p S =.11 C p C = 1 With One Exception 1. The Fittest Genotype is Eliminated. 1. The Fittest Genotype is Fixed. 2. verage Fitness goes from.9 to verage Fitness goes from.9 to % of the individuals have a relative viability of 1 and 80% have either anemia or malarial susceptibility % of the individuals have a relative viability of 1.3 and none have anemia nor malarial susceptibility. 29

30 Hb-, S and C Genotypes S SS C CS CC Viability No Malaria S is a recessive, deleterious allele relative to, so natural selection in the pre-malarial environment will keep it rare (no h 2 ). C is a neutral allele relative to, so sometimes the C allele will drift to high frequencies relative to the allele. Suppose There Was Deme With This Gene Pool Before The Malaysian gricultural Complex p = 0.95 C.045 p S =.005 Such a gene pool is likely to evolve in the pre-malarial environment because of the neutrality of and C relative to each other. 30

31 Initial Phenotypes fter Transition to Malaysian gricultural Complex Genotypes S SS C CS CC Viability Malaria Genotypic Deviation (W = 0.902) a = a S = a C = The Initial daptive Response To Malarial Environment Is To Increase The Frequency of The S and C lleles. Gene Pool fter Several Generations of Selection Under Malarial Environment p = 0.78 S.05 C 0.17 Genotypes S SS C CS CC Viability Malaria Genotypic Deviation (W = 0.914)

32 10/16/12 Gene Pool fter Several Generations of Selection Under Malarial Environment a = as = ac = fter the Initial daptive Response To Malarial Environment, Natural Selection Continues to Decrease, Increase C, but Now It lso Decreases S Because as=

33 Negative Correlation Exists Between the Frequencies of the S and C alleles in Malarial Regions in frica C llele Frequency o o.o5 o.o o.o o.o o.15 S llele Frequency in 72 West frican Populations Even uniform selective pressures produce divergent adaptive responses because selection operates upon variation whose creation and initial frequencies are profoundly influenced by random factors such as mutation and drift. 33

34 lthough adaptation is often portrayed as optimizing individual or population fitness, only gametic fitness is optimized via natural selection. Individuals or demes with the highest fitness are not necessarily favored and can be actively selected against. There are many other ways in which human populations have adapted to malaria; e.g. G-6-PD Deficiency: Plasmodium oxidizes RBC NDPH from the Pentose Phosphate pathway for its metabolism. This results in a deficiency of RBC GSH, most severe in G6PD deficient individuals, leading to peroxide-induced hemolysis which curtails the development of Plasmodium. 34

35 There are many other ways in which human populations have adapted to malaria; e.g. Thalassemia: daptation generally involves many loci with different biochemical, cellular or developmental functions. Therefore, we also need to model natural selection as a polygenic process. 35

36 The Fundamental Theorem of Natural Selection Fisher was one of the first to model natural selection as a polygenic process. lthough there are many aspects of his models, the most important results are found in what he termed the fundamental theorem of natural selection. x = phenotypic value of some trait for an individual in a population f(x) = the probability distribution that describes the frequencies of x in the population. The mean phenotype is then:! x µ = xf(x)dx w(x) = the fitness of those individuals sharing a common phenotypic value x. The mean or average fitness of the population is: w = w(x)f(x)dx! x 36

37 w(x)f(x) does not in general define a probability distribution, but w(x)f(x)/ w does integrate to one and defines the probability distribution of the selected individuals. Hence, the mean phenotype of the selected individuals is: µ s = xw(x)f(x)dx! x w Let h 2 = the heritability of the trait. The response to selection is given by R=h 2 S where S=(µ s µ ), R = (µ o µ ), and µ o is the phenotypic mean of the offspring of the selected parents. When x = w, w(w) = w by definition, and μ = w. µ s = w! wf(w)dw " w w = w 2 f(w)dw " w w µ s = " ( w 2! w 2 ) + w 2 w [ ]f(w)dw w = " w ( w 2! w 2 )f(w)dw + w 2 f(w)dw w " w µ s = " ( w! w ) 2 f(w)dw + w 2 w = # 2 + w 2 w w S = µ s! µ = " 2 + w 2! w = " 2 + w 2! w 2 w w = " 2 w 37

38 When x = w, the response to selection, R, is Δ w. Hence, R = h 2 S #!w = " 2 &# a " 2 & % (% ( $ " 2 ' $ w '!w = " 2 a w Fundamental Theorem of Natural Selection Some Implications of FFTNS FIRST, natural selection can only operate when there is genetic variation associated with phenotypic variation for fitness in the population. SECOND, the only fitness effects that influence the response to natural selection are those transmissible through a gamete. THIRD, the adaptive outcome represents an interaction of fitness variation with population structure. 38

39 Some Implications of FFTNS FOURTH, selective equilibria can only occur when all the average excesses and all the average effects are zero; that is, when all gamete s have the same average fitness impact. Evolution due to natural selection stops only when there is no heritability for fitness. This in turn means that at a selective equilibrium there is no correlation between the fitness of parents and the fitness of their offspring even when there is genetic variance in the phenotype of fitness. The Equilibrium p = 0.89 S p S = S 0.20 SS 0.01 W = 0.9 W S = 1 W SS =0.2 t Equilibrium, There is Genotypic Variation in Fitness (Broad-Sense Heritability), but No Heritability (verage Effects = 0). 39

40 Some Implications of FFTNS FIFTH, natural selection acts to increase the average fitness of a population on a per generational basis. Because the additive genetic variation must be greater than or equal to zero, Δw 0 under natural selection. Because average fitness can only increase or stay the same under natural selection, the selective equilibria discussed under point four must always correspond to an average fitness local optimum. 40

41 Wright s Concept of n daptive Surface or Landscape S SS W = 0.9 W S = 1 W SS =0.2 verage Fitness 1.0 verage Fitness p Frequency of S p Frequency of S Some Implications of FFTNS SIXTH, natural selection only takes populations to local adaptive solutions and not necessarily to the adaptive state with the highest average fitness, and indeed may operate to prevent an adaptive state with higher average fitness from evolving. 41

42 Wright s Concept of n daptive Surface or Landscape a aa W = 1 W a = 0.5 W aa =0.9 verage Fitness p Frequency of Genotypes S SS C CS CC Viability Malaria C 1.25 S 1 w C S C p S p C p C 0.25 p C p S p S S 42

43 Some Implications of FFTNS SEVENTH, natural selection generally does not optimize, even in a local sense, any individual trait other than fitness itself, even if the trait contributes to fitness in a positive fashion. Given a selective equilibrium (Δ w = 0) at a local peak, let f eq (x) = the phenotypic distribution of the trait at equilibrium. Then, the average fitness and average trait at equilibrium is: w eq = w(x)f eq (x)dx! x x eq = xf eq (x)dx! x is the optimal value of trait X only if x eq w eq = w(xeq ) Use Taylor s theorem to expand w(x) around x eq : w(x)! w(x eq ) + w'(x eq )(x " x eq) w''(x eq)(x " x eq) 2 43

44 Take the average value of both sides of the Taylor s Series approximation by integrating across the equilibrium probability distribution of the trait: w eq = w(x eq )! f eq (x)dx + w "(x x eq )! ( x # x eq )f eq (x)dx + 1 2w " (x x eq )! x ( x # x eq ) 2 f eq (x)dx w eq = w(x eq ) w! (x eq )" 2 eq (x) x eq is an optimal value of trait X that maximizes w(x) when: 1. the trait has no phenotypic variance at equilibrium [σ 2 eq (x) = 0], or 2. the trait is related to fitness in a strictly linear fashion at equilibrium [w ( x eq ) = 0] Some Implications of FFTNS EIGHTH, the process of adaptation can result in the evolution of some seemingly non-adaptive traits. In general, many traits contribute to fitness, not just one. Consider the case in which two traits, say X and Y, contribute to fitness such that w(x,y) is the fitness of those individuals with trait values x and y for the two traits respectively. Then, the two-dimensional requirement for optimality of both traits is:! 2 w(x eq,y eq ) " 2!x 2 eq (x) + 2! 2 w(x eq,y eq ) Cov eq (x, y) +! 2 w(x eq,y eq ) " 2!x!y!y 2 eq (y) = 0 44

45 E.g., many human populations have adapted to malaria by increasing the frequency of the trait of hemolytic anemia. Here, natural selection favors the increase of a highly deleterious trait. Such cases are common because of pleiotropy, and indeed most of the people who die or suffer from genetic disease do so because natural selection favored the genes despite one or more pleiotropic deleterious traits. Some Implications of FFTNS NINTH, the course of adaptive evolution is strongly influenced by genetic architecture. w C w C S C S C p S p p S p p C p C S C recessive to for malarial resistance S C with 4% dominance to for malarial resistance 45

46 Common theme? Δp = pa /W 2!w = " a w The Course of daptive Evolution Is Determined By the Phenotypic Effects ssigned to GMETES, not individuals! 46